Solving a system of equations means to solve for a numerical value for unknown variables. Substitution is a special method wherein we substitute the value of one variable into an equation to get the value of other unknown variable.** Substitution Method:** Substitution is one of the methods
which is used to solve a system of equation, which requires the
following two important points to be satisfied:

1) There should be almost the similar number of equations as there would be unknown variables present in the system of equations.

2) Any one of the equations from the given two systems could be easily solved for one variable.

If the above two conditions are satisfied, then only we can use substitution as a method for solving a system of equations.

If there are two variables, there must be two equations; three variables, three equations, and so on.

One of the equations from the given two systems could be easily solved for one variable is the main idea of substitution method.

To solve a system of equations with two variables we require the following steps:

y = –4x + 24, now we will substitute it for "y" in the first equation, and solve for x, that is, 2x – 3 (–4x + 24) = –2 or 2x + 12x – 72 = –2 or 14x = 70, this implies:

x = 5.

Now y = –4(5) + 24 = –20 + 24 = 4

Hence, the solution is (x, y) = (5, 4).

Putting it in, x + y = 20, we will get 10 + y + y = 20 or 10 + 2y = 20, that is,

2y = 10 or y = 5.

Replacing y into x + y = 20 gives x + 5 = 20, that is x = 15.

Hence, the solution to the system is x = 15 and y = 5.

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